Ello! When you downloaded the new patch from the Downloads page, did you make sure to move the .exe you downloaded into your main FeralHeart folder? You'll need to download and install FH (if you haven't already of course), then move the new .exe file into the main folder. I find it best to delete the .exe that already is in the folder after downloading, then move the new .exe over.
Also, welcome back to FeralHeart~
Awesome!! If you are not using the Play Game tab, then yes it's on your end. You'll have to log into the Play Game tab >here< (https://feral-heart.com/login/) and keep the tab open while you play in order to connect, and stay connected~